Introduction
Materials
- Description of data set
Methods
- Data cleaning and wrangling
- Vizualization
- Modelling
Results
- Data visualization
- Logistic regression
- PCA
- K-means clustering
11th May 2021
Outline
Introduction
Introduction
- Prostate cancer data set from Andrews DF and Herzberg AM (1985)
- Compare four different treatments
- 502 observations of 18 variables
- 27 NA values
Materials
The data set
The Raw Data set
| Variable Name | Desription | Level / Summary Statistic |
|---|---|---|
| patno | Patient number |
|
| rx | Dosage of estrogen treatment in mg | Placebo, 0.2 mg, 1.0 mg, 5.0 mg |
| status | Status of the patient, alive or or cause of death | alive, dead - prostatic ca, dead - heart or vascular, dead - cerebrovascular, dead - pulmonary embolus, dead - other ca, dead - respiratory disease, dead - other specific non-ca, dead - unspecified non-ca, dead - unknown cause |
| pf | Activity level based on time in bed | normal activity, in bed < 50% daytime, in bed > 50% daytime, confined to bed |
| bm | The presence of Bone Metastases | Yes/No |
| hx | History of Cardiovascular Disease | Yes/No |
| ekg | Electrocardiography | normal, benign, rhythmic disturb & electrolyte ch, heart block or conduction def, heart strain, old MI, recent MI |
The Data set
| Variable Name | Desription | Level / Summary Statistic |
|---|---|---|
| stage | Stage of prostate cancer | 3 or 4 |
| age | Age of patient in years | 71.51 (48.00 ~ 89.00) |
| wt | Weight Index = wt(kg)-ht(cm)+200 | 98.93 (69.00 ~ 152.00) |
| sbp | Systolic Blood Pressure/10 | 14.35 (8.00 ~ 30.00) |
| dbp | Diastolic Blood Pressure/10 | 8.15 (4.00 ~ 18.00) |
| hg | Serum Hemoglobin [g/100ml] | 13.45 (5.90 ~ 21.20) |
| sz | Size of Primary Tumor [cm^2] | 14.57 (0.00 ~ 69.00) |
| ap | Serum Prostatic Acid Phosphatase | 12.18 (0.01 ~ 999.88) |
| sdate | Date of study |
|
| sg | Combined Index of Stage and Hist. Grade |
|
| dtime | Months of Follow-up |
|
Methods
Methods, Data cleaning and wrangling
Raw data to Clean data
- Exclude dtime, sdate and sg
- Renaming variables
Clean data to Augment data
- Add five new variables:
- outcome = mutating status into alive vs dead
- treatment_mg = making a numeric variable by removing string
- EKG_lvl = creating a factorized variable with the levels in numbers
- performance_lvl = creating a factorized variable with the levels in numbers
- age_group = forming two age groups young/old based on the mean
Methods
Visualization of pre-treatment variables - Numeric
Methods
Visualization of pre-treatment variables - Categorical
Methods
Visualization of pre-treatment variables - Heatmap
Methods
Modelling
- Logistic regression
- PCA
- K-means clustering
Results
Results
Treatment, outcome and age
Results
Logistic model - Outcome as function of treatment
Output:
log_mod_treatment
## # A tibble: 4 x 5 ## term estimate std.error statistic p.value ## <chr> <dbl> <dbl> <dbl> <dbl> ## 1 (Intercept) 1.11 0.211 5.27 0.000000136 ## 2 treatment_mg0.2 0.0907 0.301 0.301 0.763 ## 3 treatment_mg1 -0.807 0.280 -2.88 0.00394 ## 4 treatment_mg5 -0.0536 0.294 -0.182 0.855
Results
Logistic model for each variable - Treatment = 1.0 mg
Results
Logistic model for each variable - Treatment = 1.0 mg
Results
Distribution of significant variables for each outcome
Results
Principal Component Analysis
Results
Principal Component Analysis
Results
Principal Component Analysis
Results
Principal Component Analysis
Results
K-means clustering
Results
K-means clustering
Results
K-means clustering
K-means clustering
Discussion and conclusion
Discussion and conclusion
- Stage 3 and 4 patients differ in tumor size and acid phosphatase levels
- Most effective treatment is 1.0 mg estrogen
- Significant variables are tumor size, CVD, age, and weight index
- Based on PCA, bone_mets,tumor_size and stage have strongly corralation.
- CVD and hemglobin, dbp and sbp have relationship separately
- and they both have relationship with weight_index.
- Therefore, the reason resulting in dealth could have 3 class:healthy situation, cancer and age.
- If the treatment is helpful to improve surval, it is unclear.